Non-contact method and apparatus for on-line interconnect characterization in VLSI circuits

ABSTRACT

A system that facilitates non-invasive in-line characterization of parameters of VLSI circuit interconnects is provided. A plurality of micro-electro-mechanical system (MEMS) cantilevers apply voltage(s) to VLSI circuit interconnect(s) without physical contact thereto. A measuring component measures deflection characteristics of the cantilevers, the deflection(s) correspond to electrical forces generated from the applied voltage(s) as passed through VLSI circuit interconnect(s). A component computes characteristics of the VLSI interconnect based at least in part upon the measured deflection characteristics.

TECHNICAL FIELD

The present invention generally relates to characterization ofcapacitance and resistance relating to interconnects within VLSIcircuits. More particularly, the present invention relates tonon-contact in-line characterization of capacitance and resistance ofVLSI circuit interconnects.

BACKGROUND OF THE INVENTION

Manufacturing and production of integrated circuits is a multi-billiondollar industry. A substantial amount of resources are utilized inconnection with improving performance of integrated circuits, increasingyield, and increasing density of integrated circuits. For example,aggressive scaling (miniaturization) of devices has resulted ininterconnect lines that are denser and shorter in width than everbefore. As signals are delivered through interconnect lines, parasiticcapacitance between the interconnect lines can become problematic due tocross talk and wire delays that are associated with such capacitance andresistance. If parasitic capacitance and resistance are not properlycharacterized and understood, cross talk and wire delays can compromiseintegrity and performance of the circuit. Accordingly, it is imperativethat characteristics of interconnect parasitic capacitances beunderstood, measured, modeled, and controlled. Moreover, it is importantto characterize all interconnect parasitic capacitances and resistanceswithin a VLSI circuit in order to determine whether or not such elementsfall outside bounds of design specifications and to characterize VLSItechnology.

While there have been monumental advances related to increasing densityof VLSI circuits, systems and/or methods of characterizing interconnectswithin VLSI circuits have not experienced such advances. For example,while interconnect capacitance exists (and thus can theoretically bemeasured) during fabrication of VLSI circuits, conventional systemsand/or methodologies only measure interconnect capacitance afterfabrication of a VLSI circuit has been completed. Characterization isthen performed via directly contacting probes with large pads (80–100μm) connected to the interconnects. The pads have to be large enough toenable positioning of a probe with an optical microscope. Moreover,conventional systems and/or methodologies require expensive,complicated, and sizeable testing structures to obtain measurementsrelating to capacitance of interconnects within VLSI circuits. Suchconventional systems and/or methodologies are further associated withvarious other shortcomings, such as an inability to obtain in-linecapacitance measurements due to a requirement for large pad area.Furthermore, contacting interconnects with probes can damageinterconnect surfaces, thus compromising operability of VLSI circuits.

Scanning probe microscopy was developed to alleviate some of theaforementioned deficiencies by reducing size of a probe required tocontact interconnect surfaces for both imaging and measuring parametersof the interconnects being tested. A direct contact measurement of smallcapacitances related to interconnects, however, is problematic ascapacitance of cantilevers attached to probes are similar in magnitudeor larger than parasitic interconnect capacitances desirably measured.Furthermore, oxide resident upon interconnect surfaces and tips ofcantilevers can reduce accuracy of capacitance measurements.

In view of at least the above, there exists a strong need in the art fora system and/or methodology facilitating improved characterization ofVLSI interconnect capacitance.

SUMMARY OF THE INVENTION

The following presents a simplified summary of the invention in order toprovide a basic understanding of some aspects of the invention. Thissummary is not an extensive overview of the invention. It is intended toneither identify key or critical elements of the invention nor delineatethe scope of the invention. Its sole purpose is to present some conceptsof the invention in a simplified form as a prelude to the more detaileddescription that is presented later.

As utilized in the following description, the term “characterization”refers to measurement of capacitance related to VLSI circuitinterconnects, measurement of resistance related to VLSI circuitinterconnects, and/or measurement of physical parameters related to VLSIcircuit interconnects. The present invention facilitates in-linecharacterization of VLSI circuit interconnects, which alleviates severalof the deficiencies of conventional systems and/or methods forcharacterizing VLSI circuit interconnects. For example, correctiveaction regarding a particular VLSI circuit can be taken prior to thecircuit being deemed irreparable, thus increasing yield. Furthermore,the present invention can characterize VLSI circuit interconnectswithout requiring contact thereto, thus mitigating problems associatedwith contact measuring devices (e.g., damage to interconnect lines,compromised measurements due to capacitance of a probe, . . . ).Moreover, the system and/or methodology of the present inventionrequires substantially less space than that required by conventionalsystems and/or methodologies (e.g., a need for large test structures ismitigated).

The present invention employs two or more micro-electro-mechanicalsystems (MEMS) cantilevers with disparate resonant frequencies that canbe employed to relay particular voltages to VLSI circuit interconnectswithout requiring contact with such VLSI circuit interconnects. Forexample, positioning components can position the MEMS cantileversproximate to the VLSI circuit interconnects. Moreover, the MEMScantilevers can include a conductive tip that enables voltages to berelayed from a voltage source to the VLSI circuit interconnects via theconductive tip. In accordance with one aspect of the present invention,the MEMS cantilever body can be employed as a conductive path from avoltage source to the conductive tip. Alternatively, a conductive pathcan be provided on the MEMS cantilever to facilitate an injection ofcurrents into VLSI circuit interconnects.

Voltage drops that exist between the conductive tips and the VLSIcircuit interconnects can produce electrostatic forces that cause theMEMS cantilevers to mechanically oscillate. A measuring system can beemployed to sense and/or measure the mechanical oscillations for givenvoltages (e.g., disparate voltages applied between the VLSI circuitinterconnects and the cantilever tips will generate differing mechanicaloscillations). The measuring system can be any suitable measuringsystem. For example, a deflection detector can include a bridge and apiezoresistor located on a cantilever. A computing component canthereafter determine various parameters of the VLSI circuitinterconnects based at least in part upon the mechanical oscillations.For example, parasitic capacitance, coupling capacitance betweeninterconnects, capacitance between an interconnect and a ground planewithin a substrate, physical parameters of the interconnect, etc. canall be computed and/or analyzed in accordance with one aspect of thepresent invention.

In accordance with another aspect of the present invention, a series ofdisparate voltages can be delivered to different MEMS cantilevers toobtain a robust characterization of VLSI circuit interconnects. Forexample, a single voltage source can comprise a plurality of differentoutputs, wherein each output can output voltages with differing voltagesand frequencies. One or more switches can then be employed to effectuateselectively providing a conductive tip of the MEMS cantilever with anappropriate voltage. Alternatively, a plurality of disparate voltagesources can be employed to deliver differing voltages to separateconductive tips. In accordance with one particular aspect of the presentinvention, disparate voltages can be applied which cause only one MEMScantilever to oscillate at its natural mechanical resonance, or,alternatively, at a selected frequency that provides optimal accuracyand resolution. A series of such voltages can be applied, andcomputations can be completed on mechanical oscillations resulting fromsuch voltages, thereby effectuating a robust characterization of theVLSI circuit interconnects.

To the accomplishment of the foregoing and related ends, the inventionthen, comprises the features hereinafter fully described andparticularly pointed out in the claims. The following description andthe annexed drawings set forth in detail certain illustrative aspects ofthe invention. These aspects are indicative, however, of but a few ofthe various ways in which the principles of the invention may beemployed and the present invention is intended to include all suchaspects and their equivalents. Other objects, advantages and novelfeatures of the invention will become apparent from the followingdetailed description of the invention when considered in conjunctionwith the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a system that facilitates characterizationof VLSI circuit interconnects in accordance with an aspect of thepresent invention.

FIG. 2 is a block diagram of a system that facilitates positioning andcharacterization of VLSI circuit interconnects in accordance with anaspect of the present invention.

FIG. 3 is a representative flow diagram that illustrates a methodologythat facilitates characterization of VLSI circuit interconnects inaccordance with one aspect of the present invention.

FIG. 4 is a block diagram of a system that facilitates characterizationof VLSI circuit interconnects in accordance with an aspect of thepresent invention.

FIG. 5 is an exemplary arrangement of a MEMS cantilever and a tuningfork in accordance with an aspect of the present invention.

FIG. 6 is a cross-sectional presentation of an exemplary layering ofmetals and dielectrics to provide for shielding a conductive path inaccordance with an aspect of the present invention.

FIG. 7 is an exemplary schematic in accordance with an aspect of thepresent invention.

FIG. 8 illustrates a plurality of disparate test structures that can beemployed in connection with the present invention.

FIGS. 9–18 are illustrations of an exemplary voltage source anddisparate voltages that can be applied to MEMS cantilevers in accordancewith an aspect of the present invention.

FIG. 19 is a representative flow diagram that illustrates a methodologythat facilitates characterization of VLSI circuit interconnects inaccordance with an aspect of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is now described with reference to the drawings,wherein like reference numerals are used to refer to like elementsthroughout. In the following description, for purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of the present invention. It may be evident, however, thatthe present invention may be practiced without these specific details.In other instances, well-known structures and devices are shown in blockdiagram form in order to facilitate describing the present invention.

As used in this application, the term “computer component” is intendedto refer to a computer-related entity, either hardware, a combination ofhardware and software, software, or software in execution. For example,a computer component may be, but is not limited to being, a processrunning on a processor, a processor, an object, an executable, a threadof execution, a program, and/or a computer. By way of illustration, bothan application running on a server and the server can be a computercomponent. One or more computer components may reside within a processand/or thread of execution and a component may be localized on onecomputer and/or distributed between two or more computers.

Turning now to FIG. 1, a system 100 that facilitates in-linecharacterization of physical parameters related to VLSI circuitinterconnects, including parasitic capacitance, coupling capacitancebetween VLSI circuit interconnects, etc. is illustrated. As used in thisapplication, the term “interconnects” is intended to refer tointerconnect lines, which can be metal or poly-silicon that is part ofactive devices (e.g., a transistor) or passive devices, contacts, vias,ground signal paths, or a combination thereof. Those skilled in the artcan apply the illustrated system 100 to measurements some other VLSItest structures for characterization/monitoring purposes. The system 100provides for improved characterization of physical parameters relatingto VLSI circuit interconnects while not requiring a probe tip tophysically contact VLSI circuit interconnects to obtain qualitymeasurements. The system 100 of the present invention provides forsubstantial benefits over conventional systems, including an ability tocharacterize VLSI circuit interconnects prior to completion offabrication, thus enabling in-line correction and/or control offabrication of VLSI circuits. Furthermore, operability of VLSI circuitinterconnects is not compromised due to physical damage caused by probescontacting VLSI circuit interconnects. The system 100 comprises avoltage source 102 that relays AC voltages to at least two MEMScantilevers 104 and 106, respectively. The cantilevers 104 and 106 eachcomprise conductive tips (not shown), and are further designed to havedisparate natural resonant frequencies. In accordance with one aspect ofthe present invention, the natural resonant frequencies can be less than200 kHz. Furthermore, the natural resonance of the MEMS cantilevers 104and 106 can have a ratio of approximately between 1.1 and 1.3. The MEMScantilevers 104 and 106 are positioned relative to VLSI circuitinterconnects 108, wherein a conductive tip of the MEMS cantilever 104is positioned proximate to the VLSI circuit interconnects 108 on a sideof the VLSI circuit interconnects 108 and a conductive tip of the MEMScantilever 106 is positioned proximate to the VLSI circuit interconnects108 on a substantially opposite side of the VLSI circuit interconnects108. AC voltages received by the MEMS cantilevers 104 and 106 aredelivered to the conductive tips of the MEMS cantilevers 104 and 106,which then inject AC current(s) into the VLSI circuit interconnects 108.Physical parameters (e.g., capacitance) of the VLSI circuitinterconnects 108 alter the voltages that are initially delivered acrossthe VLSI circuit interconnects 108, which are thereafter received by theconductive tips of the MEMS cantilevers 104 and 106. The MEMScantilevers thereafter mechanically oscillate due to electrical forcesresulting from AC voltages injected into the VLSI circuit interconnects108.

Mechanical oscillations 110 and 112 of each MEMS cantilever 104 and 106are sensed and relayed to an analysis component 114, which facilitatescharacterization of the VLSI circuit interconnect(s) based at least inpart upon the mechanical oscillations 110 and 112. For example, givenparticular voltages delivered to the MEMS cantilevers 104 and 106,resultant mechanical oscillations 110 and 112 can be employed by theanalysis component 114 to obtain a measurement of coupling capacitancebetween VLSI circuit interconnects. Furthermore, the analysis component114 can utilize mechanical oscillations 110 and 112 of the MEMScantilevers 104 and 106 to determine capacitance between one or moreVLSI circuit interconnects 108 and a substrate (acting as ground) inwhich the VLSI circuit interconnects 108 reside. Moreover, parasiticcapacitances can be computed by the analysis component 114 based atleast in part on the mechanical oscillations 110 and 112 resulting fromparticular sinusoidal voltages delivered by the voltage source 102 tothe MEMS cantilevers 104 and 106. The voltage source 102 can be employedto output disparate AC voltages (magnitude and frequency) to the MEMScantilevers 104 and 106. Injecting the VLSI circuit interconnects 108with a plurality of AC currents effectuates robust calculations ofparameters relating to the VLSI circuit interconnects 108. For instance,a series of disparate AC currents can be injected into the VLSI circuitinterconnects 108 to facilitate characterization of the VLSI circuitinterconnects 108. Furthermore, maintaining a particular AC voltagedelivered to the MEMS cantilever 104 while altering AC voltagesdelivered to the MEMS cantilever 106 can provide for characterization ofVLSI circuit interconnects.

In accordance with another aspect of the present invention, the MEMScantilever 104 can be designed in a manner to enable a conductive tip(not shown) associated with the MEMS cantilever 104 to contact the VLSIcircuit interconnects 108 while the conductive tip (not shown)associated with the MEMS cantilever 106 does not contact the VLSIcircuit interconnects 108. The contacting MEMS cantilever 104 can bepositioned in such a manner to substantially mitigate damage and/orcontamination that is associated with conventionalcontact-characterization systems and/or methodologies. In such amodality, fewer disparate AC voltages can be injected into the VLSIcircuit interconnects 108 while maintaining a robust characterization ofsuch interconnects 108. Furthermore, the analysis component 114 canretain the mechanical oscillations 110 and 112 resulting from aplurality of disparate AC voltages induced on the VLSI circuitinterconnects 108 in order to further calculate and/or analyzeparameters of the VLSI circuit interconnects 108. For example, theanalysis component 114 can be employed to trend data and analyze suchtrended data relating to the VLSI circuit interconnects 108.Furthermore, the analysis component 114 can effectuate automatic controland/or correction of VLSI circuit manufacturing process steps based atleast in part upon the mechanical oscillations 110 and 112 (e.g.,trended data can indicate particular manufacturing steps that needand/or do not need correction).

In accordance with another aspect of the present invention, the MEMScantilevers 104 and 106 can be piezo-resistive cantilevers, which enablethe cantilevers 104 and 106 to be self-sensing (e.g., can sensemechanical oscillations occurring on the cantilevers) and/orself-actuating. For instance, an alteration in resistance of thecantilevers 104 and 106 is indicative of deflection at a free end of thecantilevers 104 and 106. Moreover, a sensitivity to force can becomputed as a fractional change in resistance for a given force appliedat a free end of the cantilevers 104 and 106. Piezo-resistivecantilevers further can be employed in both contact and non-contactmodalities.

In accordance with one aspect of the present invention, mechanicaloscillations of the MEMS cantilevers 104 and 106 can be sensed by alaser-detection system. For example, a laser light can be directed froma laser and delivered by an integrated light guide to a MEMS cantilever,and a photo detector can be employed to capture laser light deflectionfrom/by the cantilevers. Alternatively, an optical interferometer can beemployed in connection with sensing mechanical oscillations existent inthe MEMS cantilevers 104 and 106. Furthermore, it is to be understoodthat the MEMS cantilevers 104 and 106 comprise a conductive tip in orderto enable AC currents to be injected into the VLSI circuitinterconnects. In accordance with one aspect of the present invention, aconductive path can be provided across the MEMS cantilevers 104 and 106to the conductive tips. Alternatively, the MEMS cantilevers 104 and 106can be of a conductive material, and the body of such MEMS cantilevers104 and 106 can be employed as a portion of a conductive path to theconductive tips.

The system 100 enables measurement of particularly small capacitancesexistent in interconnects 108. For example, the system 100 enablesmeasurement of capacitances as small as 1 fF. Moreover, particularlysmall interconnects can be characterized utilizing the system 100. Forinstance, the interconnect lines 108 can be less than 10 μm, and spacebetween two interconnects can be less than 0.2 μm. Moreover, portion(s)of the interconnects 108 can be on disparate layers of a VLSI circuit,and can further be covered by a dielectric layer.

Referring now to FIG. 2, a system 200 that facilitates in-linecharacterization of VLSI circuit interconnects is illustrated. Thesystem 200 includes a voltage source 202 that provides a plurality of ACvoltages to MEMS cantilevers 204 and 206, wherein the MEMS cantilevershave disparate natural resonance frequencies. The MEMS cantilevers 204and 206 are positioned proximate to VLSI circuit interconnects 208,thereby enabling conductive tips (not shown) associated with the MEMScantilevers 204 and 206 to inject the VLSI circuit interconnects 208with AC currents provided by the voltage source 202. The MEMScantilevers 204 and 206 positioned proximate to the VLSI circuitinterconnects 208 by positioning components (e.g., scanners) 210 and212, respectively. Injection of AC currents into the VLSI circuitinterconnects 208 results in electrical forces applied to the MEMScantilevers 204 and 206, thus causing such MEMS cantilevers 204 and 206to oscillate. Mechanical oscillations 214 and 216 are sensed and relayedto an analysis component 218, which effectuates robust characterizationof the VLSI circuit interconnects 208 based at least in part upon themechanical oscillations 214 and 216.

The analysis component 218 includes a computing component 220 thateffectuates calculating measurements relating to the VLSI circuitinterconnects 208 based at least in part upon voltages applied to theMEMS cantilevers 204 and 206 as well as mechanical oscillations 214 and216 resulting from such voltages. Furthermore, position of the MEMScantilevers 204 and 206 with respect to the VLSI circuit interconnects208 can also be employed by the computing component 220 in connectionwith calculating various parameters relating to the VLSI circuitinterconnects 208. Calculations that can be made by the computingcomponent 220 will be described in greater detail herein.

The analysis component 218 is further associated with a controlcomponent 222 that can utilize the mechanical oscillations 214 and 216,the voltages applied to the MEMS cantilevers 204 and 206, as well ascalculation made by the computing component 220 to control thepositioning components 210 and 212 as well as fabrication process steps.For instance, the control component can effectuate alteration ofposition of the MEMS cantilevers 204 and 206 with respect to the VLSIcircuit interconnects 208 via relaying control commands/signals to thepositioning components 210 and 212. Furthermore, the control component222 can effectuate feed-forward and/or feedback control of variousprocess steps. For example, calculations by the computing component 220can be analyzed by the control component 222 to determine if anydeviation and/or faults related to the VLSI circuit interconnects exist(e.g., whether parameters are sufficiently within designspecifications). Based at least in part upon such calculations, thecontrol component 222 can determine which fabrication process steprequires adjustment to effectuate optimal fabrication of a VLSI circuit.Moreover, as the VLSI circuit interconnects 208 can be characterizedin-line, the control component 222 can adjust later fabrication processsteps to ensure that VLSI circuit fabrication is optimized. Inaccordance with one aspect of the present invention, the positioningcomponents 210 and 212, the MEMS cantilevers 204 and 206, and the VLSIcircuit interconnects 208 can be positioned within a vacuum chamber.

Turning now to FIG. 3, a methodology 300 for characterizing VLSI circuitinterconnects during fabrication without requiring probes to contactsuch interconnects is illustrated. While, for purposes of simplicity ofexplanation, the methodology 300 is shown and described as a series ofacts, it is to be understood and appreciated that the present inventionis not limited by the order of acts, as some acts may, in accordancewith the present invention, occur in different orders and/orconcurrently with other acts from that shown and described herein. Forexample, those skilled in the art will understand and appreciate that amethodology could alternatively be represented as a series ofinterrelated states or events, such as in a state diagram. Moreover, notall illustrated acts may be required to implement a methodology inaccordance with the present invention.

At 302, MEMS cantilevers are positioned in proximity to VLSI circuitinterconnects that are desirably tested. The cantilevers are positionedin a manner to allow AC currents to enter the interconnects withoutrequiring physical contact thereto. In accordance with one aspect of thepresent invention, the cantilevers can be piezo-resistive cantilevers.Alternatively, the cantilevers can be positioned upon a tuning fork.Moreover, one cantilever can be provided with a contact probe thatenables contact to a first VLSI circuit interconnect and does notoscillate, while a second cantilever does not contact any VLSIinterconnect and can oscillate. Providing one of the cantilevers incontact with one interconnect can facilitate a more expedientcharacterization of the interconnects.

At 304, AC currents are injected into the interconnects via tips of theMEMS cantilevers. In accordance with one aspect of the presentinvention, a series of disparate AC currents can be selectively injectedinto the VLSI circuit interconnects to facilitate a robustcharacterization of the interconnects. Moreover, a voltage source cancomprise a plurality of outputs for outputting disparate voltages, andswitches can be employed to provide each cantilever with disparate ACvoltages (amplitude and/or frequency). The voltage drops between thecantilever tip and the interconnect result in electrical forces thatcause the MEMS cantilevers to oscillate.

At 306, existent oscillations on the MEMS cantilevers caused by theinjection of AC currents into the interconnects are measured. Inaccordance with one aspect of the present invention, the MEMScantilevers can be self-sensing, thereby facilitating sensing and/ormeasurement of mechanical oscillation existent on the cantilevers.Furthermore, pre-amplifiers and amplifiers can be provided to amplifyelectrical signals produced by the mechanical oscillations to facilitatemeasurement and analysis of such oscillations. In accordance with oneaspect of the present invention, mechanical oscillations relating to aseries of disparate voltages applied to the cantilever tips can bemeasured and employed in connection with characterizing VLSI circuitinterconnects.

At 308, the mechanical oscillations are employed to characterize theVLSI circuit interconnects. For example, physical parameters of the VLSIcircuit interconnects can be measured and analyzed based at least inpart upon the sensed mechanical oscillations given particular voltagesapplied to the cantilever tips. Moreover, coupling capacitance betweenVLSI circuit interconnects can be determined, as well as capacitancebetween a VLSI circuit interconnect and a substrate (acting as ground).In accordance with another aspect of the present invention, parasiticcapacitance and/or resistance related to the VLSI circuit interconnectscan be monitored and analyzed. Such a methodology 300 providessignificant improvement over conventional systems in that the VLSIcircuit interconnects can be characterized in-line. Further, ohmiccontact between a probe and the interconnects is not required when themethodology 300 is employed.

Now regarding FIG. 4, a system 400 that facilitates in-linecharacterization of VLSI circuit interconnects without requiring a probeto contact such interconnects is illustrated. The system 400 includes avoltage source 402 that is employed to deliver AC voltages to MEMScantilevers 404 and 406, wherein the cantilevers 404 and 406 areassociated with disparate natural resonance frequencies. The AC voltagescan be delivered to the MEMS cantilevers 404 and 406 via switches 408and 410, which enable disparate AC voltages to be delivered to the MEMScantilevers 404 and 406 by the single voltage source 402. Providing aplurality of disparate AC voltages to the MEMS cantilevers 404 and 406enables robust characterization of VLSI circuit interconnects. Theswitches 408 and 410 can be controlled by a control component 412. Forinstance, the voltage source 402 can comprise a plurality of outputs,and the control component 412 can effectuate positioning of the switches408 and 410 in a manner wherein desirable outputs of the voltage source402 are relayed to the MEMS cantilevers 404 and 406.

The MEMS cantilevers 404 and 406 can be positioned on tuning forks 414and 416, respectively. The tuning forks 414 and 416 can be self-sensing(e.g., they can sense mechanical oscillations occurring on the tuningforks 414 and 416) and/or self-actuating. For example, the tuning forks414 and 416 can be quartz tuning forks. In accordance with one aspect ofthe present invention, the MEMS cantilevers 404 and 406 are generatedwith a pair of legs, wherein each leg is attached to one prong of thetuning fork. Moreover, bodies of the cantilevers 404 and 406 can serveas a portion of the conductive path from the voltage source 402 to thetips (not shown) of the MEMS cantilevers 404 and 406. However, theconductive path must be shielded from the tuning fork bodies, which canbe effectuated, for example, by providing grounded electrodes to serveas electrostatic shields. More particularly, three layers of metal canbe employed, wherein a first layer is tuning fork body electrodes, asecond layer is a shielded electrode, and a third layer is a conductivepath to allow AC voltages to be delivered to the MEMS cantilevers 404and 406.

Desirable AC voltages can thus be delivered from the voltage source 402to the MEMS cantilevers 404 and 406 via the switches 408 and 410. The ACcurrents can then be injected into VLSI circuit interconnects 418, whichresults in generation of electrical forces that cause the tuning forks414 and 416 to oscillate. Pre-amplifiers 420 and 422 and amplifiers 424and 426 can be employed to amplify electrical signals produced bymechanical oscillations, which are indicative of particular parametersof the VLSI circuit interconnects 418. The amplified electrical signalscan then be received by an analysis component 428 that facilitatescharacterization of the VLSI circuit interconnects 418. The analysiscomponent can be associated with a computing component 430 thatcalculates one or more parameters of the VLSI circuit interconnects 418based at least in part upon the amplified oscillations. Moreover, thecontrol component 412 can control one or more fabrication process stepsbased at least in part upon measurements calculated by the computingcomponent 428.

Now regarding FIG. 5, an exemplary tuning fork 500 that can be employedin connection with the present invention is illustrated. A MEMScantilever 502 with a pair of legs can be positioned upon the tuningfork 500 to provide a first leg of the cantilever 502 on a first prongof the tuning fork 500 and a second leg of the cantilever 502 on asecond leg of the tuning fork 500. The MEMS cantilever 502 can becoupled to a voltage source (not shown) via pads 504 and a conductivepath 506. Furthermore, the MEMS cantilever 502 should also beconductive, thereby allowing voltages to travel through such cantilever502 and into VLSI circuit interconnects (not shown). For instance, theMEMS cantilever 502 can be composed of a metal that is substantiallysimilar to a metal utilized in the conductive path 506. The tuning fork500 can be self-sensing and/or self-actuating, thereby mitigating arequirement for expensive sensing equipment. More particularly, thetuning fork 500 can be a quartz tuning fork in accordance with oneparticular aspect of the present invention.

Turning briefly to FIG. 6, a cross section of the tuning fork 500 isillustrated. The conductive path 506 should be shielded from a body ofthe tuning fork 500 via grounded electrodes that can serve as anelectrostatic shield. For example, the tuning fork 500 can include threedisparate layers of metal, wherein a first layer 508 is employed astuning fork electrodes, a second layer 510 is employed as a shieldedelectrode, and a third layer is the conductive path 506. The layers ofmetal are separated by dielectric layers 512 and 514 (e.g., a layerbetween the tuning fork electrodes 508 and the shielding electrodes 510,and a layer between the shielding electrodes 510 and the conductive path506). Moreover, while not illustrated with respect to FIGS. 5 and 6, itis to be understood that the output pads 504 (FIG. 5) should be locatedproximate to the tuning fork electrode output pads (not shown) in orderto effectuate generation of an electrostatic shield. Furthermore, it isto be understood that the cantilever 502 (FIG. 5) can be fastened to thetuning fork 500 via any acceptable means (e.g., glue).

Now turning to FIG. 7, an exemplary schematic 700 of a system that canbe employed in connection with the present invention is illustrated. Theschematic 700 includes a pair of voltage sources 702 and 704 that areutilized to deliver AC voltages to a pair of MEMS cantilevers 706 and708. While the exemplary schematic 700 displays two voltage sources 702and 704, it is to be understood that a single voltage source coupled totwo or more switches can be employed to create a substantially similarschematic. AC voltages delivered by the voltage sources 702 and 704create AC currents that are injected into a pair of VLSI circuitinterconnects 710 and 712 via the MEMS cantilevers 706 and 708. The ACcurrents induce AC voltages on the pair of VLSI circuit interconnects710 and 712. In such an embodiment, the interconnects 710 and 712 can becharacterized in-line, and contact to such interconnects 710 and 712with probes is not required. Moreover, coupling capacitances between theMEMS cantilevers 706 and 708 and the interconnects 710 and 712 as wellas coupling capacitances between the interconnects 710 and 712 andadjacent interconnects can be neglected. Turning briefly to FIG. 8, aplurality of test structures 800–810 are illustrated. The interconnects710 and 712 (FIG. 7) can be positioned and/or shaped in a manner toenable testing of the subject invention (e.g., the interconnects 710 and712 can be utilized as test structures 800–810). Moreover, resultsobtained via the test structures can be employed as empirical data andutilized in connection with characterizing interconnects that are notpositioned and/or shaped in a similar manner to the test structures800–810. Exemplary locations of conductive tips 812 and 814 of the MEMScantilevers 706 and 708 (FIG. 7), respectively, are further illustratedon the interconnects 710 and 712. Moreover, a line 816 is displayed withrespect to test structure 810 that connects the test structure 810 to aground of the substrate. The distance α between disparate ends of thetest structures can be approximately 1 μm. The test structure 810illustrates a plurality of disparate locations that the conductive tip814 can be located on the interconnect 712 in connection withcharacterizing the VLSI interconnects 710 and 712.

A described theory below is intended to illustrate exemplary modalitiesof operation from a simulation/optimization viewpoint for teststructures similar to those shown in FIG. 8. These exemplary teststructures are part of the subject invention, as they have beendeveloped to minimize all parasitic capacitances between the cantilevers706, 708 and the interconnects 710 and 712. Furthermore, although oneparticular set of test structures have been illustrated, many other teststructures or fragments of a real product interconnects can be utilizedfor process performance characterization.

During instances that AC signals of less than approximately 300 kHz areemployed, and transmission line effects can be neglected, thecapacitance matrix of the cantilevers-interconnects system whereinterconnects can be the lines of the test structures shown in FIG. 8can be written as:

$\lbrack C\rbrack = \left\lbrack \begin{matrix}C_{11} & {- C_{12}} & {- C_{13}} & 0 \\{- C_{12}} & C_{22} & 0 & {- C_{24}} \\{- C_{13}} & 0 & C_{33} & 0 \\0 & {- C_{24}} & 0 & C_{44}\end{matrix} \right\rbrack$where C₁₁=C_(1g)+C₁₂+C₁₃, C₂₂=C_(2g)+C₁₂+C₂₄, C₃₃=C_(3g)+C₁₃. andC₄₄=C_(4g)+C₂₄. AC voltages V₃ and V₄ are applied to tips (not shown) ofthe MEMS cantilevers 706 and 708, thereby causing an AC current to flowthrough the VLSI circuit interconnects 710 and 712 to ground. PotentialsU₁ and U₂ are induced by such current flow, such that V₁ and V₂ can bewritten as V₁=U₁+ΔΦ and V₂=U₂+ΔΦ, where ΔΦ is a time independentcomponent of a potential of the VLSI circuit interconnects 710 and 712that depend upon material of the interconnects 710 and 712.

The potentials U₁ and U₂ for interconnects comprising the abovecapacitance matrix can be written as U₁=Ψ₁ ⁽³⁾V₃+Ψ₁ ⁽⁴⁾V₄, and Ψ₂⁽³⁾V₃=Ψ₂ ⁽⁴⁾V₄, respectively, where Ψ₁ ⁽³⁾, Ψ₁ ⁽⁴⁾, Ψ₂ ⁽³⁾ and Ψ₂ ⁽⁴⁾are functions of capacitances C₁₁, C₂₂, C₁₂, C₁₃ and C₂₄, and for thesmall amplitudes of the mechanical oscillations one can write:

${\Psi_{1}^{(3)} = \frac{C_{22}C_{13}}{D}},{\Psi_{2}^{(3)} = \frac{C_{12}C_{13}}{D}},{\Psi_{1}^{(4)} = \frac{C_{12}C_{24}}{D}},{\Psi_{2}^{(4)} = \frac{C_{11}C_{24}}{D}},$where D=C₁₁C₂₂−C₁₂ ². The AC potentials V₃ and V₄ are harmonic, and canbe defined by equations V₃=V₃₀ sin(Ω₃t) and V₄=V₄₀ sin(Ω₄t), where Ω₃and Ω₄ are angular frequencies. V₁₀, V₂₀, V₃₀, V₄₀, V₅₀, V₆₀, and V₇₀are amplitudes of voltages that can be output from a voltage source.Such amplitudes can be pre-defined or empirically determined. Viasubstitution, equations for induced potentials U₁ and U₂ can be writtenas U₁=V₃₀Ψ₁ ⁽³⁾ sin(Ω₃t)+V₄₀Ψ₁ ⁽⁴⁾ sin(Ω₄t) and U₂=V₃₀Ψ₂ ⁽³⁾sin(Ω₃t)+V₄₀Ψ₂ ⁽⁴⁾ sin(Ω₄t).

Existent voltage drops between the MEMS cantilevers 706 and 708 and theVLSI circuit interconnects 710 and 712 produces electrostatic forces F₃and F₄, respectively, that can deflect the cantilevers 706 and 708. Withrespect to time, the electrostatic forces F₃(t) and F₄(t) can be definedas a summation of seven components: electrostatic forces F_(3,ΔΦ) andF_(4,ΔΦ) and six time-dependent harmonic electrostatic forces withfrequencies Ω₃, Ω₄, 2 Ω₃, 2 Ω₄,Ω₃+Ω₄ and Ω₄−Ω₃. For example,F₃(t)±F_(3,ΔΦ)+F+F_(3,ΔΦΩ) ₃ sin Ω₄t+F_(3,2) Ω ₃ cos 2 Ω₃t+F_(3,2) Ω ₄cos 2 Ω₄t+F_(3,Ω) ₄ _(±Ω) ₃ [cos (Ω₃+Ω₄)t+cos(ψ₄−Ω₃)t], andF₄(t)±F_(4,ΔΦ)+F_(4,ΔΦ,Ω) ₃ sin Ω₃t+F_(4,ΔΦ,Ω) ₄ sin Ω₄t+F_(4,2Ω) ₃ cos2 Ω₃t+F_(4,2Ω) ₄ cos 2 Ω₄t+F_(4,Ω) ₄ _(±Ω) ₃ [cos(Ω₃+Ω₄)t+cos(Ω₄+Ω₃)t].Given the above schematic 700 and capacitance matrix, amplitudes of theelectrostatic force components can be defined as follows:

${F_{3,{2\Omega_{3}}} = {V_{10}^{2}\left\lbrack {\frac{\partial C_{3g}}{\partial d_{1}} + {\left( {1 - {2\Psi_{1}^{(3)}} + \Psi_{1}^{{(3)}^{2}}} \right)\frac{\partial C_{13}}{\partial d_{1}}} - {2\left( {1 - \Psi_{1}^{(3)}} \right){C_{13}\left( \frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}} \right)}}} \right\rbrack}};$${F_{3,{2\Omega_{4}}} = {V_{20}^{2}\left\lbrack {{\left( \Psi_{1}^{(4)} \right)^{2}\frac{\partial C_{13}}{\partial d_{1}}} + {2\left( \Psi_{1}^{(4)} \right)C_{13}\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}}}} \right\rbrack}};$${F_{3,{\Omega_{4} \pm \Omega_{3}}} = {{- 2}V_{30}{V_{40}\left\lbrack {{\left( {1 - \Psi_{1}^{(3)}} \right)\Psi_{1}^{(4)}\frac{\partial C_{13}}{\partial d_{1}}} + {\left( {\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}} - {\Psi_{1}^{(3)}\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}}} - {\Psi_{1}^{(4)}\frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}}}} \right)C_{13}}} \right\rbrack}}};$${F_{3,{\Delta\Phi},\Omega_{3}} = {\Delta\;{\Phi \cdot {V_{60}\left\lbrack {{\left( {1 - \Psi_{1}^{(3)}} \right)\frac{\partial C_{13}}{\partial d_{1}}} - {C_{13}\frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}}}} \right\rbrack}}}};$${F_{3,{\Delta\Phi},\Omega_{4}} = {{- \Delta}\;{\Phi \cdot {V_{60}\left\lbrack {{\Psi_{1}^{(4)}\frac{\partial C_{13}}{\partial d_{1}}} + {C_{13}\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}}}} \right\rbrack}}}};$${F_{4,{2\Omega_{3}}} = {V_{10}^{2}\left\lbrack {{{\Psi_{2}^{(3)}}^{2}\frac{\partial C_{24}}{\partial d_{2}}} + {2\Psi_{2}^{(3)}{C_{24}\left( \frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}} \right)}}} \right\rbrack}};$${F_{4,{2\Omega_{4}}} = {V_{20}^{2}\left\lbrack {\frac{\partial C_{4g}}{\partial d_{2}} + {\left( {1 - {2\Psi_{2}^{(4)}} + \Psi_{2}^{{(4)}^{2}}} \right)\frac{\partial C_{24}}{\partial d_{2}}} - {2\left( {1 - \Psi_{2}^{(4)}} \right){C_{24}\left( \frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}} \right)}}} \right\rbrack}};$${F_{4,{\Omega_{4} \pm \Omega_{3}}} = {{- 2}V_{30}{V_{50}\left\lbrack {{\left( {1 - \Psi_{2}^{(4)}} \right)\Psi_{2}^{(3)}\frac{\partial C_{24}}{\partial d_{2}}} + {\left( {\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}} - {\Psi_{2}^{(4)}\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}}} - {\Psi_{2}^{(3)}\frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}}}} \right)C_{24}}} \right\rbrack}}};$${F_{4,{\Delta\Phi},\Omega_{3}} = {{- \Delta}\;{\Phi \cdot {V_{70}\left\lbrack {{\Psi_{2}^{(3)}\frac{\partial C_{24}}{\partial d_{2}}} + {C_{24}\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}}}} \right\rbrack}}}};$${F_{4,{\Delta\Phi},\Omega_{4}} = {\Delta\;{\Phi \cdot {V_{70}\left\lbrack {{\left( {1 - \Psi_{2}^{(4)}} \right)\frac{\partial C_{24}}{\partial d_{2}}} - {C_{24}\frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}}}} \right\rbrack}}}};$${{F_{3,{\Delta\Phi}} = {\frac{1}{2}{\Delta\Phi}^{2}\frac{\partial C_{13}}{\partial d_{1}}}};{{{and}\mspace{14mu} F_{4,{\Delta\Phi}}} = {\frac{1}{2}{\Delta\Phi}^{2}\frac{\partial C_{24}}{\partial d_{2}}}}},{{{where}{\frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}} = {\frac{{- C_{22}^{2}}C_{13}}{D^{2}}\left\lbrack {{\frac{\partial C_{13}}{\partial d_{1}}\left( {1 - \frac{D}{C_{13}C_{22}}} \right)} + \frac{\partial C_{1g}}{\partial d_{1}}} \right\rbrack}}};{\frac{\partial\Psi_{2}^{(3)}}{\partial d_{1}} = {\frac{{- C_{12}}C_{13}C_{22}}{D^{2}}\left\lbrack {\frac{\partial C_{1g}}{\partial d_{1}} + {\left( {1 - \frac{D}{C_{13}C_{22}}} \right)\frac{\partial C_{13}}{\partial d_{1}}}} \right\rbrack}};{\frac{\partial\Psi_{1}^{(3)}}{\partial d_{2}} = {\frac{{- C_{11}}C_{13}C_{22}}{D^{2}}\left( {1 - \frac{D}{C_{11}C_{22}}} \right)\left( {\frac{\partial C_{2g}}{\partial d_{2}} + \frac{\partial C_{24}}{\partial d_{2}}} \right)}};{\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}} = {\frac{{- C_{12}}C_{13}C_{11}}{D^{2}}\left( {\frac{\partial C_{24}}{\partial d_{2}} + \frac{\partial C_{2g}}{\partial d_{2}}} \right)}};{\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}} = {\frac{{- C_{12}}C_{24}C_{22}}{D^{2}}\left\lbrack {\frac{\partial C_{13}}{\partial d_{1}} + \frac{\partial C_{1g}}{\partial d_{1}}} \right\rbrack}};}$${\frac{\partial\Psi_{2}^{(4)}}{\partial d_{1}} = {\frac{{- C_{11}}C_{24}C_{22}}{D^{2}}\left( {1 - \frac{D}{C_{11}C_{22}}} \right)\left( {\frac{\partial C_{13}}{\partial d_{1}} + \frac{\partial C_{1g}}{\partial d_{1}}} \right)}};$${\frac{\partial\Psi_{1}^{(4)}}{\partial d_{2}} = {\frac{{- C_{12}}C_{24}C_{11}}{D^{2}}\left\lbrack {\frac{\partial C_{2g}}{\partial d_{2}} + {\left( {1 - \frac{D}{C_{24}C_{11}}} \right)\frac{\partial C_{24}}{\partial d_{2}}}} \right\rbrack}};$${\frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}} = {\frac{{- C_{24}}C_{11}^{2}}{D^{2}}\left\lbrack {{\frac{\partial C_{24}}{\partial d_{2}}\left( {1 - \frac{D}{C_{24}C_{11}}} \right)} + \frac{\partial C_{2g}}{\partial d_{2}}} \right\rbrack}};$where

$\frac{\partial C_{2g}}{\partial d_{2}},\frac{\partial C_{1g}}{\partial d_{1}},{\frac{\partial C_{24}}{\partial d_{2}}\mspace{14mu}{and}\mspace{14mu}\frac{\partial C_{13}}{\partial d_{1}}}$are unknown capacitances that can be obtained bysolving above equations, while the additional unknowns, ΔΦ and

$\frac{\partial C_{3g}}{\partial d_{1}},\frac{\partial C_{4g}}{\partial d_{2}}$can be found during system calibration.

Under an influence of the forces F₃ (t) and F₄ (t) the MEMS cantilevers706 and 708 will oscillate simultaneously on next frequencies Ω₃, Ω₄, 2Ω₃, 2 Ω₄, Ω₃+Ω₄ and Ω₄–Ω₃ if frequencies Ω₃ and Ω₄ of the ac voltages V₃and V₄ are not equal. To simplify computations, the frequencies Ω₃ andΩ₄ of the AC voltages V₃ and V₄ can be selected to enable only one MEMScantilever to oscillate at its natural mechanical resonance. Mechanicalresonance of the MEMS cantilevers 706 and 708 can be produced by theplurality of harmonic electrostatic forces represented by aboveequations if its frequency is substantially similar to the resonantfrequency of a cantilever or any other suitable selected frequency.Harmonic forces F_(3R) and F_(4R) that force the cantilevers 706 and708, respectively, to oscillate at their mechanical resonance or anyother suitable selected frequency can be written as F_(3R)=F₃₀sin(Ω_(res5)t) and F_(4R)=F₄₀ sin(ω_(res6)t), where ω_(res5) andω_(res6) are angular resonant or suitable selected frequencies of theMEMS cantilevers 706 and 708, respectively, and F₃₀, F₄₀ are forceamplitudes.

If A and B are resonant oscillation amplitudes of the MEMS cantilevers706 and 708, respectively, they can be defined as follows: A=g_(c5)F₃₀and B=_(c6)F₄₀, where g_(c5) and g_(c6) represent transfer functionsbetween force amplitudes F₃₀ and F₄₀ and the oscillation amplitudes Aand B of the cantilevers 706 and 708, respectively: In accordance withone aspect of the present invention, the transfer functions g_(c5) andg_(c6) can be obtained empirically by observing alterations inamplitudes of A and B and comparing the amplitudes with known forceamplitudes acting on tips (not shown) of the MEMS cantilevers 706 and708.

Amplitudes of output resonance sensed by a sensing component (not shown)and amplified by one or more amplifiers (not shown) are related to theoscillation amplitudes A and B by equations V_(I)=g₁A and V_(II)=g₂B,where g₁ and g₂ represent transfer functions between oscillationamplitudes A and B of the MEMS cantilevers 706 and 708, respectively,and output signal amplitudes V_(I) and V_(II) sensed by sensors andamplified by amplifiers. Such transfer functions can be obtainedempirically by observing alterations in amplitudes V_(I) and V_(II) andcomparing such amplitudes with known oscillation amplitudes of tips (notshown) of the MEMS cantilevers 706 and 708. Via substitution, relationsbetween amplitudes V_(I), V_(II), F₃₀, and F₄₀ can be seen in thefollowing equations: V₁=μg₁g_(c5)F₃₀ and V_(II)=g₂g_(c6)F₄₀. There tendisparate independent combinations of amplitudes and frequencies of ACvoltages V₃ and V₄ that can be applied to tips (not shown) of thecantilevers 706 and 708 that force only a single cantilever to oscillateat the resonance. While the above analysis has been described withparticular specificity with respect to allowing only one cantilever tooscillate, it is to be understood that such an embodiment is merelyexemplary. Any system that employs multiple cantilevers thatmechanically oscillate upon deliverance of a voltage across proximateVLSI circuit interconnects is contemplated by the present invention andintended to fall within the scope of the hereto-appended claims.Moreover, the computing component 220 (FIG. 2) can complete any of theabove calculations to output desirable calculations.

Turning now to FIGS. 9–17, an exemplary system 900 that facilitatesin-line characterization of VLSI circuit interconnects without requiringcontact thereto is illustrated. The figures illustrate a series of ACvoltages that can be applied to a pair of cantilevers to effectuaterobust characterization of VLSI circuit interconnects, includingmeasurement of coupling capacitance between interconnects, measurementof capacitance between an interconnect and a substrate (acting asground), and measurement of parasitic capacitance. Moreover, the FIGS.9–17 illustrate a methodology for obtaining five measurements of V_(I)and V_(II) as discussed supra.

Referring first to FIG. 9, the system 900 comprises a voltage source 902that delivers sinusoidal voltages to a pair of MEMS cantilevers 904 and906 via switches 908 and 910, respectively. The sinusoidal voltages arethen injected into a pair of VLSI circuit interconnects 912 and 914,which result in generation of electrostatic forces that can cause one orboth of the MEMS cantilevers 904 and 906 to oscillate. The resultingoscillations can be monitored to facilitate characterization of the VLSIcircuit interconnects 912 and 914. A first measurement of V_(I) can beobtained when the switch 908 connects an output O1 of the voltage source902 to a conductive tip (not shown) of the MEMS cantilever 904 (e.g.,the MEMS cantilever can be conductive, or only a tip of the MEMScantilever can be conductive). The output voltage has amplitude of V₁₀and a frequency that is substantially similar to half of the resonancefrequency f_(res5) of the cantilever 904. A conductive tip (not shown)of the MEMS cantilever 906 is connected to ground, thereby placing thecantilever 906 out of resonance and the cantilever 904 within resonance.Thus V₁=g₁g_(c5)F_(3,2Ω) ₃ .

Turning now to FIG. 10, a measurement of V_(II) is obtained. Anamplitude of V_(II) can be measured when the switch 908 connects aconductive tip of the MEMS cantilever 904 to output O2 of the voltagesource 902 and the switch 910 connects a conductive tip of the MEMScantilever 906 to ground. The voltage output from output O2 hasamplitude of V₂₀ and frequency that is substantially equal to half ofthe resonance frequency f_(res6) of the MEMS cantilever 906. Therefore,during such a measurement the cantilever 904 is out of resonance whilethe cantilever 906 is at resonance. Thus V_(II)=g₂g_(c6)F_(4,2Ω) ₃ .

Now referring to FIG. 11, a measurement of V_(I) can be obtained. Anamplitude of V_(I) is measured when the switch 908 connects a conductivetip of the MEMS cantilever 904 to ground and the switch 910 connects aconductive tip of the MEMS cantilever 906 to output O1. The voltageoutput from output O1 has amplitude of V₁₀ and frequency that issubstantially similar to half of the resonance frequency f_(res5) of thecantilever 906. Therefore, during such a measurement the cantilever 906is out of resonance and the cantilever 904 is at resonance. Thus,V₁=g₁g_(c5)F_(3,2Ω) ₄ .

Turning now to FIG. 12, a measurement of V_(II) can be obtained. Anamplitude of V_(II) is measured when the switch 908 connects aconductive tip of the MEMS cantilever 904 to ground and the switch 910connects a conductive tip of the MEMS cantilever 906 to output O2. Thevoltage output form the output O2 has amplitude of V₂₀ and frequencythat is substantially similar to half of the resonance frequencyf_(res6) of the cantilever 908. Therefore, during such measurement thecantilever 904 is out of resonance and the cantilever 906 is atresonance. Thus, V_(II)=g₂g_(c6)F_(4,2Ω) ₄ .

Now regarding FIG. 13, a measurement of V_(I) can be obtained. Anamplitude of V_(I) is measured when the switch 908 connects a conductivetip of the MEMS cantilever 904 to output O3 and the switch 910 connectsa conductive tip of the MEMS cantilever 906 to the output O4 of thevoltage source 902. The voltage output from the output O3 has amplitudeof V₃₀ and a frequency f₃, and the output O4 has an amplitude V₄₀ and afrequency f₄ that is substantially similar to the resonance frequencyf_(res5) of the cantilever 904 plus a frequency f₃ (f₄=f_(res5)+f₃),where f₃ is substantially similar to bf_(res6), and wherein b≧1.3.Alternatively, the frequency f₄ can be substantially similar to f_(res5)(1+ab), and also can be substantially similar to

${\frac{f_{res6}}{a}\left( {1 + {ab}} \right)},$wherein

$a = {\frac{f_{res6}}{f_{res5}}.}$Therefore, during such measurement the cantilever 904 is at resonanceand the cantilever 906 is out of resonance. Thus, V₁=μg₁g_(c5)F_(3,Ω) ₄_(±) ₃ .

Turning now to FIG. 14, a measurement of V_(II) can be obtained. Anamplitude of V_(II) is measured when the switch 908 connects aconductive tip of the MEMS cantilever 904 to the output O3 of thevoltage source 902 and the switch 910 connects a conductive tip of theMEMS cantilever 906 to the output O5. The voltage output from the outputO3 has amplitude of V₃₀ and frequency of f₃, and the voltage output fromthe output O5 has amplitude of V₅₀ and frequency f₅ that is equal to theresonance frequency f_(res6) of the MEMS cantilever 906 plus thefrequency f₃ (f₅=f_(res6)+f₃). Furthermore, the frequency f₅ is alsosubstantially similar to af_(res5)(1+b), as well as substantiallysimilar to f_(res6) (1+ab). Thus, during such measurement the cantilever904 is out of resonance and the cantilever 906 is at resonance. Thus,V_(II)=g₂g_(c6)F_(4,Ω) ₄ _(±Ω) ₃ .

Now regarding FIG. 15, a measurement of V₁ can be obtained. An amplitudeof V₁ is measured when the switch 908 connects a conductive tip of theMEMS cantilever 904 to the output O6 of the voltage source 902 and theswitch 910 connects a conductive tip of the MEMS cantilever 906 toground. The voltage output from the output O6 has amplitude of V₆₀ and afrequency substantially similar to the resonance frequency f_(res5) ofthe cantilever 904. Therefore, during such measurement the cantilever904 is at resonance and the cantilever 906 is out of resonance. Thus,V₁=g₁g_(c5)F_(3,ΔΦ,Ω) ₃ .

Referring now to FIG. 16, a measurement of V_(II) can be obtained. Anamplitude of V_(II) is measured when the switch 908 connects aconductive tip of the MEMS cantilever 904 to the output O7 of thevoltage source 902 and the switch 910 connects a conductive tip of theMEMS cantilever 906 to ground. The voltage output from the output O7 hasamplitude of V₇₀ and a frequency substantially similar to the resonancefrequency f_(res6) of the cantilever 906. Therefore, during suchmeasurement the cantilever 904 is out of resonance and the cantilever906 is at resonance. Thus, V_(II)=g₂g_(c6)F_(4,ΔΦ,Ω) ₃.

Turning now to FIG. 17, a measurement of V_(I) can be obtained. Anamplitude of V_(I) is measured when the switch 908 connects a conductivetip of the MEMS cantilever 904 to ground and the switch 910 connects aconductive tip of the MEMS cantilever 906 to the output O6 of thevoltage source 902. The voltage output from the output O6 has amplitudeof V₆₀ and a frequency substantially similar to the resonance frequencyf_(res5) of the cantilever 904. Therefore, during such measurement thecantilever 904 is at resonance and the cantilever 906 is out ofresonance. Thus, V₁=g₁g_(c5)F_(3,ΔΦ,Ω) ₄ .

Now referring to FIG. 18, a measurement of V_(II) can be obtained. Anamplitude of V_(II) is measured when the switch 908 connects aconductive tip of the MEMS cantilever 904 to ground and the switch 910connects a conductive tip of the MEMS cantilever to the output O7 of thevoltage source 902. The voltage output from the output O7 has amplitudeof V₇₀ and a frequency substantially similar to the resonance frequencyf_(res6) of the cantilever 906. Therefore, during such measurement thecantilever 904 is out of resonance and the cantilever 906 is atresonance. Thus, V_(II)=g₂g_(c6)F_(4,ΔΦ,Ω) ₄ .

From such ten measurements, the computing component 220 (FIG. 2) cancalculate forces F_(3,2Ω) ₃ , F_(4,2Ω) ₃ etc. as discussed with respectto FIG. 7. Such forces can in turn be employed to calculate capacitancesC₁₂, C_(1g), and C_(2g) as illustrated in FIG. 7.

Returning to FIG. 7, measurement of capacitances C₁₂ and C_(2g) can beperformed when a conductive tip (not shown) of the MEMS cantilevers 706contacts one the interconnect 710 the MEMS cantilever 708 does notcontact the interconnect 712. In such an instance, only measurementstaken with respect to FIGS. 10, 12, 14, 16, and 18 are necessary tocalculate the aforementioned capacitances. From such five measurementsof V_(II), electrostatic force components (e.g., F_(4,2Ω) ₃ , F_(4,2Ω) ₄, . . . ) can be calculated, which in turn can be employed to calculateC₁₂ and C_(2g). For instance, the equations

${F_{4,{2\Omega_{3}}} = {V_{10}^{2}\left\lbrack {{\Psi_{2}^{{(3)}^{2}}\frac{\partial C_{24}}{\partial d_{2}}} + {2\Psi_{2}^{(3)}{C_{24}\left( \frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}} \right)}}} \right\rbrack}},{F_{4,{2\Omega_{4}}} = {V_{20}^{2}\left\lbrack {\frac{\partial C_{4g}}{\partial d_{2}} + {\left( {1 - {2\Psi_{2}^{(4)}} + \Psi_{2}^{{(4)}^{2}}} \right)\frac{\partial C_{24}}{\partial d_{2}}} - {2\left( {1 - \Psi_{2}^{(4)}} \right){C_{24}\left( \frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}} \right)}}} \right\rbrack}},{F_{4,{\Omega_{4} \pm \Omega_{3}}} = {{- 2}V_{30}{V_{50}\left\lbrack {{\left( {1 - \Psi_{2}^{(4)}} \right)\Psi_{2}^{(3)}\frac{\partial C_{24}}{\partial d_{2}}} + {\left( {\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}} - {\Psi_{2}^{(4)}\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}}} - {\Psi_{2}^{(3)}\frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}}}} \right)C_{24}}} \right\rbrack}}},{F_{4,{\Delta\Phi},\Omega_{3}} = {{- \Delta}\;{\Phi \cdot {V_{70}\left\lbrack {{\Psi_{2}^{(3)}\frac{\partial C_{24}}{\partial d_{2}}} + {C_{24}\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}}}} \right\rbrack}}}},{and}$${F_{4,{\Delta\Phi},\Omega_{4}} = {\Delta\;{\Phi \cdot {V_{70}\left\lbrack {{\left( {1 - \Psi_{2}^{(4)}} \right)\frac{\partial C_{24}}{\partial d_{2}}} - {C_{24}\frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}}}} \right\rbrack}}\mspace{14mu}{can}\mspace{14mu}{be}\mspace{14mu}{employed}\mspace{14mu}{to}\mspace{14mu}{calculate}\mspace{14mu}{capacitances}\mspace{11mu} C_{12}\mspace{14mu}{and}\mspace{14mu} C_{2g}}},{where}$${\Psi_{2}^{(3)} = \frac{C_{12}}{C_{2g} + C_{24} + C_{12}}},{\Psi_{2}^{(4)} = \frac{C_{24}}{C_{2g} + C_{24} + C_{12}}},{\frac{\partial\Psi_{2}^{(3)}}{\partial d_{2}} = {\frac{- C_{12}}{\left( {C_{2g} + C_{24} + C_{12}} \right)^{2}}\left\lbrack {\frac{\partial C_{24}}{\partial d_{2}} + \frac{\partial C_{2g}}{\partial d_{2}}} \right\rbrack}},{and}$$\frac{\partial\Psi_{2}^{(4)}}{\partial d_{2}} = {{\frac{- C_{24}}{\left( {C_{2g} + C_{24} + C_{12}} \right)^{2}}\left\lbrack {{\frac{\partial C_{24}}{\partial d_{2}}\left( {1 - \frac{C_{2g} + C_{24} + C_{12}}{C_{24}}} \right)} + \frac{\partial C_{2g}}{\partial d_{2}}} \right\rbrack}.}$

Alternatively, capacitances C₁₂ and C_(1g) can be calculated when aconductive tip of the MEMS cantilever 706 does not contact theinterconnect 710 while a conductive tip of the MEMS cantilever 708contacts the interconnect 712. In such an instance, only measurementstaken with respect to FIGS. 9, 11, 13, 15, and 17 are necessary tocalculate the aforementioned capacitances. From such five measurementsof V_(I), electrostatic force components (e.g., F_(3,2Ω) ₃ , F_(3,2Ω) ₄, . . . ) can be calculated, which in turn can be employed to calculateC₁₂ and C_(1g). For example, the equations

${F_{3,{2\Omega_{3}}} = {V_{10}^{2}\left\lbrack {\frac{\partial C_{3g}}{\partial d_{1}} + {\left( {1 - {2\Psi_{1}^{(3)}} + \Psi_{1}^{{(3)}^{2}}} \right)\frac{\partial C_{13}}{\partial d_{1}}} - {2\left( {1 - \Psi_{2}^{(3)}} \right){C_{13}\left( \frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}} \right)}}} \right\rbrack}},{F_{3,{2\Omega_{4}}} = {V_{20}^{2}\left\lbrack {{\left( \Psi_{1}^{(4)} \right)^{2}\frac{\partial C_{13}}{\partial d_{1}}} + {2\left( \Psi_{1}^{(4)} \right)C_{13}\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}}}} \right\rbrack}},{F_{3,{\Omega_{4} \pm \Omega_{3}}} = {{- 2}V_{30}{V_{40}\left\lbrack {{\left( {1 - \Psi_{1}^{(3)}} \right)\Psi_{1}^{(4)}\frac{\partial C_{13}}{\partial d_{1}}} + {\left( {\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}} - {\Psi_{1}^{(3)}\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}}} - {\Psi_{1}^{(4)}\frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}}}} \right)C_{13}}} \right\rbrack}}},{F_{3,{\Delta\Phi},\Omega_{3}} = {\Delta\;{\Phi \cdot {V_{60}\left\lbrack {{\left( {1 - \Psi_{1}^{(3)}} \right)\frac{\partial C_{13}}{\partial d_{1}}} - {C_{13}\frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}}}} \right\rbrack}}}}\mspace{11mu},{and}$$F_{3,{\Delta\Phi},\Omega_{4}} = {{- \Delta}\;{\Phi \cdot {V_{60}\left\lbrack {{\Psi_{1}^{(4)}\frac{\partial C_{13}}{\partial d_{1}}} + {C_{13}\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}}}} \right\rbrack}}\mspace{14mu}{can}\mspace{14mu}{be}\mspace{14mu}{employed}\mspace{14mu}{to}\mspace{14mu}{calculate}\mspace{14mu} C_{12}\mspace{14mu}{and}\mspace{14mu} C_{1g}}$where${\Psi_{1}^{(3)} = \frac{C_{13}}{C_{1g} + C_{12} + C_{13}}},{\Psi_{1}^{(4)} = \frac{C_{12}}{C_{1g} + C_{12} + C_{13}}},{\frac{\partial\Psi_{1}^{(4)}}{\partial d_{1}} = {\frac{- C_{12}}{\left( {C_{1g} + C_{13} + C_{12}} \right)^{2}}\left\lbrack {\frac{\partial C_{13}}{\partial d_{1}} + \frac{\partial C_{1g}}{\partial d_{1}}} \right\rbrack}},{and}$$\frac{\partial\Psi_{1}^{(3)}}{\partial d_{1}} = {{\frac{- C_{13}}{\left( {C_{1g} + C_{13} + C_{12}} \right)^{2}}\left\lbrack {{\frac{\partial C_{13}}{\partial d_{1}}\left( {1 - \frac{C_{1g} + C_{13} + C_{12}}{C_{13}}} \right)} + \frac{\partial C_{1g}}{\partial d_{1}}} \right\rbrack}.}$

Turning now to FIG. 19, a methodology 1900 for applying a plurality ofdisparate voltages to conductive tips of MEMS cantilevers that arepositioned proximate to VLSI circuit interconnects. The methodologyfacilitates measuring a plurality of capacitances related to VLSIcircuit interconnects, and thus facilitates characterization of suchVLSI circuit interconnects. In accordance with one aspect of the presentinvention, one of the conductive tips can contact a VLSI circuitinterconnect while a conductive tip of a second MEMS cantilever does notcontact a VLSI circuit interconnect. Alternatively, the conductive tipsof both MEMS cantilevers do not contact the VLSI circuit interconnects.

At 1902, a particular voltage is applied to a first MEMS cantilever. Forexample, a voltage with frequency substantially equivalent to a resonantfrequency of the cantilever can be applied to such cantilever.Furthermore, the MEMS cantilever can be attached to ground (thusapplying a zero voltage to the MEMS cantilever). Moreover, voltages withany suitable amplitude and any suitable frequency can be applied to thefirst MEMS cantilever. At 1904, a particular voltage is applied to asecond MEMS cantilever. Such application of voltages generate mechanicaloscillations on the MEMS cantilevers. In accordance with one aspect ofthe present invention, voltages can be selectively applied to the firstand second MEMS cantilevers to cause only a single cantilever tomechanically oscillate at resonant frequencies.

At 1906, a determination is made regarding whether a measurement ofV_(I) or V_(II) is desirable. A computing component and/or controlcomponent can facilitate a determination of which measurement isdesirably taken (and which voltages to deliver to the MEMS cantilevers).If V_(I) is desirably measured, at 1908 such measurement is completed.If V_(II) is desirably measured, at 1910 such measurement is completed.At 1912, a determination is made regarding whether a sufficient numberof measurements have been obtained. For example, in a non-contactmodality, ten measurements (five of V_(I) and five of V_(II)) may berequired to facilitate robust characterization of a pair of VLSI circuitinterconnects. Alternatively, in a contact modality, five measurementsof either V_(I) and V_(II) may be necessary to robustly characterizecapacitance of VLSI circuit interconnects. If more measurements aredesirable, the methodology repeats. If sufficient measurements have beentaken, then at 1914 capacitance measurements can be calculated.Equations discussed supra can be employed in connection with calculatingcapacitance.

What has been described above includes examples of the presentinvention. It is, of course, not possible to describe every conceivablecombination of components or methodologies for purposes of describingthe present invention, but one of ordinary skill in the art mayrecognize that many further combinations and permutations of the presentinvention are possible. Accordingly, the present invention is intendedto embrace all such alterations, modifications and variations that fallwithin the spirit and scope of the appended claims. Furthermore, to theextent that the term “includes” is used in either the detaileddescription or the claims, such term is intended to be inclusive in amanner similar to the term “comprising” as “comprising” is interpretedwhen employed as a transitional word in a claim.

1. A system that facilitates non-invasive in-line characterization ofparameters of VLSI circuit interconnects, comprising: a plurality ofmicro-electro-mechanical system (MEMS) cantilevers that apply voltage(s)to VLSI circuit interconnect(s) without physical contact thereto; ameasuring component that measures deflection characteristics of thecantilevers, the deflection(s) correspond to electrical forces generatedfrom the applied voltage(s) as passed through VLSI circuitinterconnect(s); and a component that computes characteristics of theVLSI interconnect based at least in part upon the measured deflectioncharacteristics.
 2. The system of claim 1, further comprising a controlcomponent that effectuates control of a VLSI circuit fabrication processstep based at least in part upon the computed characteristics.
 3. Thesystem of claim 2, the computed characteristics are employed as feedbackinformation to the control component.
 4. The system of claim 2, whereinthe computed characteristics are employed as feed-forward information tothe control component.
 5. The system of claim 1, the MEMS cantileverscomprise conductive tips to effectuate injection of voltages into theVLSI circuit interconnects.
 6. The system of claim 5, the MEMScantilevers act as a conductive path to the conductive tips.
 7. Thesystem of claim 5, a conductive path is provided on the MEMS cantileversto the conductive tips to facilitate injection of currents into the VLSIcircuit interconnects.
 8. The system of claim 1, further comprising teststructures for capacitance and/or resistance measurement.
 9. The systemof claim 1, further comprising a voltage source that delivers voltagesto the MEMS cantilevers, the voltage source delivering disparatevoltages to disparate MEMS cantilevers.
 10. The system of claim 1, themeasuring component comprising a photo-detector that detects a laserbeam deflecting off at least one MEMS cantilever.
 11. The system ofclaim 1, the measuring component comprises an optical interferometer.12. The system of claim 1, further comprising a positioning componentthat facilitates proper positioning of the MEMS cantilevers with respectto the VLSI circuit interconnects.
 13. The system of claim 12, theposition components being scanners.
 14. The system of claim 1, furthercomprising a pre-amplifier.
 15. The system of claim 1, furthercomprising an amplifier.
 16. The system of claim 1, further comprising atuning fork, at least one MEMS cantilever is attached to the tuningfork.
 17. The system of claim 16, the tuning fork is a quartz tuningfork that can be at least one of self-sensing and self-actuating. 18.The system of claim 16, an electrostatic shield is provided to shield aconductive path across the tuning fork to a conductive tip of the MEMScantilever.
 19. The system of claim 16, a first leg of the MEMScantilever is attached to a first prong of the tuning fork, and a secondleg of the MEMS cantilever is attached to a second prong of the tuningfork.
 20. The system of claim 1, at least one MEMS cantilever is apiezo-resistive cantilever.
 21. The system of claim 1, employed tomeasure coupling capacitance between VLSI circuit interconnects.
 22. Thesystem of claim 1, employed to measure capacitance between at least oneVLSI circuit interconnect and a ground plane.
 23. The system of claim 1,the MEMS cantilevers and the VLSI circuit interconnects are within avacuum chamber.
 24. The system of claim 1, utilized to characterize atleast one of resistance and capacitance of a transistor.
 25. The systemof claim 1, a distance between VLSI circuit interconnects is less than0.2 μm.
 26. The system of claim 1, a length of VLSI circuitinterconnects is less than 10 μm.
 27. The system of claim 1, at least aportion of a first VLSI circuit interconnect to be tested is on adisparate layer compared to a second VLSI circuit interconnect to betested.
 28. The system of claim 1, the VLSI circuit interconnects arecovered by a layer of dielectric.
 29. A system that facilitatescharacterization of VLSI circuit interconnects, comprising: a voltagesource that outputs a plurality of disparate voltages; two or moremicro-electro-mechanical system (MEMS) cantilevers that receive thevoltages output by the voltage source and apply the voltage(s) to VLSIcircuit interconnect(s), wherein a first MEMS cantilever contacts afirst VLSI interconnect and a second MEMS cantilever does not physicallycontact a VLSI interconnect; a measuring component that measuresdeflection characteristics of the cantilevers, the deflection(s)correspond to electrical forces generated from the applied voltage(s) aspassed through VLSI circuit interconnect(s); and a component thatcomputes characteristics of the VLSI interconnect based at least in partupon the measured deflection characteristics.
 30. The system of claim29, wherein the computing component calculates a coupling capacitancebetween VLSI circuit interconnects based at least in part upon themeasured deflection characteristics.
 31. The system of claim 29, thecomputing component calculates a capacitance of a VLSI circuitinterconnect that is not contacted by the first MEMS cantilever withrespect to ground.
 32. A method that facilitates measurement of variousparameters of VLSI circuit interconnects, comprising: positioning atleast two MEMS cantilevers with conductive tips in proximity to at leasttwo adjacent VLSI circuit interconnects; providing voltage(s) to theconductive tips; injecting the current (s) into the VLSI circuitinterconnects via the conductive tips; measuring oscillations resultantin the MEMS cantilevers; and computing capacitance related to the VLSIcircuit interconnects based at least in part upon the measuredoscillations.
 33. The method of claim 32, further comprising computingcoupling capacitance between the two adjacent VLSI circuit interconnectsbased at least in part upon the measured oscillations.
 34. The method ofclaim 32, further comprising computing capacitance of at least one MEMScantilever with respect to a ground plane in a substrate.
 35. The methodof claim 32, further comprising: providing a first voltage to a firstMEMS cantilever with a frequency substantially similar to one half of atleast one of a natural resonant frequency and a user-selected frequencyof the first MEMS cantilever; and grounding a second MEMS cantilever.36. The method of claim 32, further comprising: providing a firstvoltage to a first MEMS cantilever with a frequency substantiallysimilar to one half of at least one of a natural resonant frequency anda user-selected frequency of a second MEMS cantilever; and grounding thesecond MEMS cantilever.
 37. The method of claim 32, further comprising:providing a first voltage to a first MEMS cantilever with a frequencysubstantially similar to bf_(res6), where b is a constant such thatb≧1.3 and resonance frequency (f_(res6)) is substantially similar to onehalf of at least one of a resonant frequency and a user-selectedfrequency of a second MEMS cantilever; and providing a second voltage tothe second MEMS cantilever with a frequency substantially similar tof_(res6) (1+ab), where a resonance frequency(f_(res5)) is substantiallysimilar to half a resonant frequency of the first MEMS cantilever and ais substantially similar to f_(res5)/f_(res6).
 38. The method of claim32, further comprising: providing a first voltage to a first MEMScantilever with a frequency substantially similar to bf_(res6), where bis a constant such that b≧1.3 and resonance frequency (f_(res6)) issubstantially similar to one half of at least one of a resonantfrequency and a user-selected frequency of a second MEMS cantilever; andproviding a second voltage to the second MEMS cantilever with afrequency substantially similar to f_(res6)(1+ab), wherein where a issubstantially similar to f_(res5)/f_(res6), and f_(res5) issubstantially similar to one half of at least one of a resonantfrequency and a user-selected frequency of the first MEMS cantilever.39. The method of claim 32, further comprising: providing a firstvoltage to a first MEMS cantilever with a frequency substantiallysimilar to at least one of a resonant frequency and a user-selectedfrequency of the first MEMS cantilever; and grounding a second MEMScantilever.
 40. The method of claim 32, further comprising: providing afirst voltage to a first MEMS cantilever with a frequency substantiallysimilar to at least one of a resonant frequency and a user-selectedfrequency of a second MEMS cantilever; and grounding the second MEMScantilever.
 41. The method of claim 32, further comprising controlling aVLSI circuit fabrication process based at least in part upon measuredoscillations.
 42. The method of claim 32 employed to characterize atransistor.
 43. A system for characterizing of VLSI interconnectcircuits, comprising: means for positioning two or more MEMS cantileversproximate to a pair of VLSI circuit interconnects without contactthereto; means for injecting currents into the VLSI circuitinterconnects via the MEMS cantilevers; means for measuring oscillationson the MEMS cantilevers resulting from electrostatic forces generatedupon injecting the currents; and means for computing capacitance relatedto the VLSI circuit interconnects based at least in part upon themeasured oscillations.
 44. The system of claim 43, further comprisingmeans for selectively injecting disparate currents into the VLSI circuitinterconnects.
 45. The system of claim 44, further comprising means forcalculating capacitance based at least in part upon measuredoscillations resulting from application of a plurality of disparatevoltages.